Can an American president make big, historic changes in the country’s direction with a relatively narrow base of political support? That was the challenge President Obama faced when he pushed health-care reform through Congress, and it’s the same problem he faces now in trying to win support for a breakthrough nuclear deal with Iran.

Obama was confident and combative as he made his case this week on Iran. He delivered a powerful speech enumerating the virtues of the agreement. But he included some partisan lines that riled opponents (and some fence-sitters, too), and it’s questionable whether the speech, masterful as it was in analysis, will add any votes of support.

Iran is an issue on which Obama is so hot he’s combustible. It fuses the big foreign-policy themes of his presidency: the need to work with international partners and engage adversaries; the danger of an Iraq war “mindset” that prefers military solutions to diplomatic ones. Rarely has Obama seemed so convinced that he’s right and that the contrary view, as he put it Wednesday, “doesn’t make sense.”

This moral certainty powered his speech Wednesday at American University, chosen as a venue to evoke President John F. Kennedy’s famous address there that laid the foundations for detente with the Soviet Union. Obama said he’s faced some tough decisions as president, but in this case the pros and cons are “not even close.”

On the substance, I agree with Obama. The agreement will provide clear, verifiable limits on Iran’s ability to build a nuclear weapon for at least 15 years. Those who think more sanctions can gain a better deal are, as Obama said at AU, “selling a fantasy.”

Obama’s problem is that for many members of Congress, pressured by pro-Israel lobbying groups and suspicious of Iran, the question is closer. He seems determined to ram it through, seeking just enough votes to sustain a veto of a congressional vote of disapproval. But he would be wiser to seek a broader base, say by offering a package that lets Congress monitor implementation and verification of the pact.

History tells us that big diplomatic moves abroad work best when they have solid support at home, lest they founder like Woodrow Wilson’s idealistic plan for a League of Nations. But Obama starts from the perspective that in today’s hyper-polarized Washington, such a broad consensus is impossible.

“The degree of polarization that currently exists in Washington is such where I think it’s fair to say that if I presented a cure for cancer, getting legislation passed to move that forward would be a nail-biter,” Obama told a small group of journalists Wednesday afternoon after the AU speech. It was a funny line, but I also heard a cry of despair: The president is convinced he’s right about Iran, but equally convinced that the GOP majority in Congress won’t listen. Critics seem to be speaking merely from “talking points,” he told us.

Obama was meeting journalists in the Roosevelt Room, one of the White House spaces that’s spooky with history. A portrait shows “T.R.” on horseback, the American centurion. But on a table behind Obama was a sculpture that better conveyed his current predicament: It portrayed a bison beset by wolves.

“I make it a policy not to anticipate failure,” Obama said sharply, fending off a question about whether war with Iran really was likely if Congress, despite all his arguments, rejects the Iran agreement. But then he went on for nearly 10 minutes to explain precisely why, if the agreement collapses, the United States will have no leverage other than military power.

Obama clearly sees the Iran deal as the defining foreign-policy achievement of his presidency. His model isn’t just JFK’s search for detente with the Soviets, but also President Richard Nixon’s trip to China. Obama talks the way leaders do when they think big and make a controversial decision with “hair on it,” as Obama put it. “When Nixon went to China,” Obama reminded us, “Mao was still in power. He had no idea how it was going to play out.”

Radiating from the face of this sometimes dry, distanced man was rare passion and conviction: Be bold. Engage. Take risks. Write history. “There’s no doubt that after six and a half years, I am much more confident in the assessments I make and can probably see around the corners faster,” he said.

Yes, but can he bring the country with him? On a project as important as the Iran deal, it’s worth more of an effort to build broader political support.